SIS (version 0.4)

SIS: (Iterative) Sure Independence Screening ((I)SIS) and fitting in Generalized Linear Models and Cox proportional hazards regression models

Description

This function first implements the iterative sure independence screening with functions GLMvanISISscad, GLMvanISISscad, COXvanISISscad, COXvarISISscad for different variants of (I)SIS, then gets the final regression coefficients with functions getfinalSCADcoef, INDEPgetfinalSCADcoef, getfinalSCADcoefCOX for the SCAD regularized loglikelihood for the variables picked by (I)SIS.

Usage

SIS(data=NULL, model='glm', family=NULL, method='efron', vartype=0, nsis=NULL, 
rank.method='obj', eps0=1e-5, inittype='NoPen', tune.method='BIC', folds=NULL,
post.tune.method='CV',post.tune.folds=NULL, DOISIS=TRUE, 
ISIStypeCumulative=FALSE, maxloop=5, xtune=NULL, ytune=NULL, detail=FALSE)

Arguments

data

a list that contains the data.

model

the model used, the implemented ones are 'glm' and 'cox'.

family

a description of the error distribution and link function to be used in the generalized linear model.

method

indicates how to handle observations that have tied (i.e., identical) survival times. The default "efron" method is generally preferred to the once-popular "breslow" method.

vartype

vartype specifies variant (I)SIS of first type or second type.

nsis

number of pedictors recuited by (I)SIS.

rank.method

the criterion for ranking predictor variables in (I)SIS. It can be either obj or coeff.

eps0

an effective zero relative to the scale of the maximum absolute marginal regression coefficients.

inittype

inittype specifies the type of initial solution for the one-step SCAD. It can be either NoPen or L1.

tune.method

method for tuning regularization parameter.

folds

fold information for cross validation.

post.tune.method

method for tuning regularization parameter in the final step for getting SCAD coefficients.

post.tune.folds

fold information for cross validation in the final step for getting SCAD coefficients.

DOISIS

DOISIS specifies whether to do iterative SIS.

ISIStypeCumulative

ISIStypeCumulative specifies whether to penalize variables selected by the previous step of the ISIS iteration in the following SCAD step. (ISIStypeCumulative= FALSE put penalties on all variables. In this case, the procedure is

maxloop

maximum number of loops in iterative SIS.

xtune, ytune

independent tuning dataset.

detail

indicates whether return detailed information or not. Default is FALSE.

Value

• Returns an object with
• SISind
  the vector of indices selected by SIS.
• ISISind
  the vector of indices selected by ISIS.
• SIScoef
  the vector of solution by SIS followed by SCAD.
• ISIScoef
  the vector of solution by ISIS.

References

Jianqing Fan and Jinchi Lv (2008) Sure independence screening for ultra-high dimensional feature space (with discussion) Journal of Royal Statistical Society B, 36, 849-911. Jianqing Fan, Richard Samworth, and Yichao Wu (2009) Ultrahigh dimensional variable selection: beyond the linear model Journal of Machine Learning Research, to appear. Jianqing Fan and Rui Song (2009) Sure Independence Screening in Generalized Linear Models with NP-Dimensionality, technical report.

See Also

GLMvanISISscad, GLMvanISISscad, COXvanISISscad, COXvarISISscad, getfinalSCADcoef, INDEPgetfinalSCADcoef, getfinalSCADcoefCOX

Examples

set.seed(0)
b <- c(2,2,2,-3*sqrt(2))
n=150
p=200
truerho=0.5
corrmat=diag(rep(1-truerho, p))+matrix(truerho, p, p)
corrmat[,4]=sqrt(truerho)
corrmat[4, ]=sqrt(truerho)
corrmat[4,4]=1
cholmat=chol(corrmat)
x=matrix(rnorm(n*p, mean=0, sd=1), n, p)
x=x%*%cholmat
feta=x[, 1:4]%*%b
fprob=exp(feta)/(1+exp(feta))
y=rbinom(n, 1, fprob)

xtune=matrix(rnorm(n*p, mean=0, sd=1), n, p)
xtune=xtune%*%cholmat
feta=xtune[, 1:4]%*%b
fprob=exp(feta)/(1+exp(feta))
ytune=rbinom(n, 1, fprob)

binom.result1=SIS(data=list(x=x, y=y), family=binomial(), xtune=xtune, ytune=ytune)
binom.result2=SIS(data=list(x=x, y=y), family=binomial(), xtune=xtune, ytune=ytune, 
vartype=1)
binom.result3=SIS(data=list(x=x, y=y), family=binomial(), xtune=xtune, ytune=ytune, 
vartype=2)



myrates <- exp(x[,1:4]%*%b)

ytrue <- rexp(n, rate = myrates) 
cen <- rexp(n, rate = 0.1 )
time <- pmin(ytrue, cen)
status <- as.numeric(ytrue <= cen)

cox.result1=SIS(data=list(x=x,time=time,status=status), model='cox', vartype=0)
cox.result2=SIS(data=list(x=x,time=time,status=status), model='cox', vartype=1)
cox.result3=SIS(data=list(x=x,time=time,status=status), model='cox', vartype=2)